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RROMPy/examples/Python_FreeFem++/HelmholtzLagrangeApproximantsSweep.py
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HelmholtzLagrangeApproximantsSweep.py
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#!/usr/bin/env python3
import numpy as np
from context import FreeFemHelmholtzEngine as HFEngine
from context import FreeFemHSEngine as HSEngine
from context import ROMApproximantLagrangePade as Pade
from context import ROMApproximantLagrangeRB as RB
from context import ROMApproximantSweeper as Sweeper
npoints = 31
ktars = np.linspace(0, 21, npoints)
from FreeFem_snippets import SquareHomogeneousBubble
bd, V, f = SquareHomogeneousBubble(kappa = 12**.5, theta = np.pi / 3, n = 10)
solver = HFEngine(V, 12**.5, forcingTerm = f, DirichletBoundary = "1,2,3,4")
plotter = HSEngine(solver.V)
shift = 3
nsets = 3
stride = 2
Smax = stride * (nsets - 1) + shift + 2
paramsPade = {'S':Smax, 'polyBasis':'CHEBYSHEV', 'POD':True}
paramsRB = {'S':Smax, 'nodesType':'CHEBYSHEV', 'POD':True}
paramsSetsPade = [None] * nsets
paramsSetsRB = [None] * nsets
for i in range(nsets):
paramsSetsPade[i] = {'N': stride * i + shift + 1, 'M': stride * i + shift,
'S': stride * i + shift + 2}
paramsSetsRB[i] = {'R': stride * i + shift + 1, 'S': stride * i + shift + 2}
appPade = Pade(solver, plotter, ks = [4 + .5j, 14 + .5j],
approxParameters = paramsPade)
appRB = RB(solver, plotter, ks = [4 + .5j, 14 + .5j],
approxParameters = paramsRB)
sweeper = Sweeper.ROMApproximantSweeper(ktars = ktars, mostExpensive = 'Approx')
sweeper.ROMEngine = appPade
sweeper.params = paramsSetsPade
filenamePade = sweeper.sweep('../Data/HelmholtzBubbleLagrangePadeFF.dat',
outputs = 'ALL')
sweeper.ROMEngine = appRB
sweeper.params = paramsSetsRB
filenameRB = sweeper.sweep('../Data/HelmholtzBubbleLagrangeRBFF.dat',
outputs = 'ALL')
####################
from matplotlib import pyplot as plt
for i in range(nsets):
nSamples = stride*i+shift+2
PadeOutput = sweeper.read(filenamePade, {'S':nSamples},
['kRe', 'HFNorm', 'AppNorm', 'ErrNorm'])
RBOutput = sweeper.read(filenameRB, {'S':nSamples},
['kRe', 'AppNorm', 'ErrNorm'])
ktarsF = PadeOutput['kRe']
solNormF = PadeOutput['HFNorm']
PadektarsF = PadeOutput['kRe']
PadeNormF = PadeOutput['AppNorm']
PadeErrorF = PadeOutput['ErrNorm']
RBktarsF = RBOutput['kRe']
RBNormF = RBOutput['AppNorm']
RBErrorF = RBOutput['ErrNorm']
plt.figure()
plt.semilogy(ktarsF, solNormF, 'k-', label='Sol norm')
plt.semilogy(PadektarsF, PadeNormF, 'b.--',
label='Pade'' norm, S = {}'.format(nSamples))
plt.semilogy(RBktarsF, RBNormF, 'g.--',
label='RB norm, S = {}'.format(nSamples))
plt.legend()
plt.grid()
plt.figure()
plt.semilogy(PadektarsF, PadeErrorF, 'b',
label='Pade'' error, S = {}'.format(nSamples))
plt.semilogy(RBktarsF, RBErrorF, 'g',
label='RB error, S = {}'.format(nSamples))
plt.legend()
plt.grid()
plt.figure()
plt.semilogy(ktarsF, PadeErrorF / solNormF, 'b',
label='Pade'' relative error, S = {}'.format(nSamples))
plt.semilogy(RBktarsF, RBErrorF / solNormF, 'g',
label='RB relative error, S = {}'.format(nSamples))
plt.legend()
plt.grid()
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